Finite Group Databasebeta

← C2×#21447089 #29707840

Subgroups — C2×#21447089 #29707840

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839810C211yesmaximal, characteristic, complemented
2C2×#16839779C211yesmaximal, characteristic, complemented
3C2×#16839767C211yesmaximal, characteristic, complemented
4C2×#16839746C211yesmaximal, characteristic, complemented
5C22×#14519694C211yesmaximal, characteristic, complemented
6#21447089C218yesmaximal, direct product factor
7C2×#16839534C211yesmaximal, characteristic, complemented
8C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12C2×#14519736C2211yescharacteristic
13#16839810—22no—
14#16839810C2214yescomplemented
15C2×#14519712—22no—
16#16839779—22no—
17#16839779C2214yescomplemented
18C2×#14519704—22no—
19#16839767—22no—
20#16839767C2214yescomplemented
21C2×#14519698—22no—
22#16839746—22no—
23#16839746C2214yescomplemented
24C2×#14519696—21no—
25C2×#14519694—22no—
26C2×#14519694—22no—
27C2×#14519694—21no—
28C2×#14519694C2214yescomplemented
29#16839534C2214yescomplemented
30C22×#41×C61C2211yescharacteristic
31C23×D4×C61C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C61—22no—
33C2×AGL(1,ℤ/8)×C61—22no—
34C2×AGL(1,ℤ/8)×C61—22no—
35C2×AGL(1,ℤ/8)×C61—22no—
36C2×AGL(1,ℤ/8)×C61—22no—
37C2×AGL(1,ℤ/8)×C61C2214yes—
38C22×SD16×C61—21no—
39C22×D8×C61—21no—
40C22×M16×C61C2211yescharacteristic
41C2×#11758194—21no—
42C2×#11758194—21no—
43C2×#11758194—21no—
44C2×#11758194—21no—
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194D412yes—
55C2×#11758194D412yes—
56C2×#11758194C2312yes—
57C2×#11758194C2312yes—
58C2×#11758194C2312yes—
59C22×#92418—21no—
60C22×#92418—21no—
61C22×#92418—21no—
62#14519736—21no—
63#14519736—21no—
64#14519736—21no—
65#14519736C2312yes—
66C2×C4⋊Dic61—21no—
67C2×C22⋊Dic61—21no—
68C2×C4×Dic61—21no—
69#14519712—28no—
70#14519704—28no—
71#14519698—28no—
72#14519696—24no—
73#14519694—24no—
74#14519694—28no—
75C25×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—21no—
84C2×#41×C61—21no—
85C2×#41×C61—21no—
86C2×#41×C61D412yes—
87C2×#41×C61C2312yes—
88C22×Q8×C61D411yescharacteristic
89C22×D4×C61—21no—
90C22×D4×C61—21no—
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61—21no—
100C22×D4×C61—21no—
101C22×D4×C61D411yescharacteristic
102C22×D4×C61D412yes—
103C22×D4×C61D412yes—
104C22×D4×C61C2312yes—
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107AGL(1,ℤ/8)×C61—28no—
108AGL(1,ℤ/8)×C61—28no—
109AGL(1,ℤ/8)×C61—28no—
110AGL(1,ℤ/8)×C61—28no—
111C2×SD16×C61—24no—
112C2×SD16×C61—24no—
113C2×SD16×C61—24no—
114C2×D8×C61—24no—
115C2×D8×C61—24no—
116C2×D8×C61—24no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61D412yes—
121C2×M16×C61D412yes—
122C2×M16×C61C2312yes—
123C22×C8×C61—21no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61—21no—
127C24×C61—22no—
128C24×C61—41no—
129C24×C61—41no—
130C24×C61—41no—
131C24×C61—41no—
132C24×C61—84no—
133C24×C61#4111yescharacteristic
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61C2×D412yes—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—21no—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—41no—
179C2×D4×C61—41no—
180C2×D4×C61—41no—
181C2×D4×C61—41no—
182C2×D4×C61—41no—
183C2×D4×C61—41no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—41no—
190C2×D4×C61—41no—
191C2×D4×C61—41no—
192C2×D4×C61—41no—
193C2×D4×C61—41no—
194C2×D4×C61C2×D412yes—
195C2×D4×C61C2×D414yes—
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—41no—
200C22×C4×C61—41no—
201C22×C4×C61—41no—
202C22×C4×C61—41no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61#4111yescharacteristic
212C22×C4×C61#4111yescharacteristic
213C22×C4×C61#4111yescharacteristic
214C22×C4×C61#4111yescharacteristic
215C22×C4×C61#4111yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C22×Dic61—41no—
218SD16×C61—216no—
219D8×C61—216no—
220M16×C61—22no—
221M16×C61—22no—
222M16×C61—22no—
223M16×C61C2×D414yes—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—41no—
229C4⋊Dic61—22no—
230C4⋊Dic61—41no—
231C4×Dic61—22no—
232C4×Dic61—41no—
233#11758194—22no—
234#11758194—22no—
235#11758194—22no—
236#11758194—22no—
237#11758194—22no—
238#11758194—22no—
239#11758194—22no—
240#11758194—41no—
241#11758194—41no—
242#11758194—41no—
243#11758194—41no—
244#11758194C2×D414yes—
245C2×#92418—22no—
246C2×#92418—22no—
247C2×#92418—22no—
248C2×#92418—22no—
249C2×#92418—22no—
250C2×#92418—41no—
251C2×#92418—41no—
252C2×#92418—41no—
253C2×#92418—41no—
254C23×C61—24no—
255C23×C61—22no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61—82no—
268C23×C61—84no—
269C23×C61—84no—
270C23×C61—84no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61#12111yescharacteristic
274C23×C61#12111yescharacteristic
275C23×C61#12311yescharacteristic
276C23×C61#12311yescharacteristic
277C23×C61#12411yescharacteristic
278C23×C61#12411yescharacteristic
279C23×C61C2×#4111yescharacteristic
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61—41no—
283Q8×C61—41no—
284D4×C61—22no—
285D4×C61—24no—
286D4×C61—22no—
287D4×C61—24no—
288D4×C61—42no—
289D4×C61—42no—
290D4×C61—42no—
291D4×C61—42no—
292D4×C61—42no—
293D4×C61—42no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—42no—
298D4×C61—41no—
299D4×C61—41no—
300C2×C4×C61—22no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61#12011yescharacteristic
308C2×C4×C61#12011yescharacteristic
309C2×C4×C61#12011yescharacteristic
310C2×C4×C61#12011yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12111yescharacteristic
315C2×C4×C61#12111yescharacteristic
316C2×C4×C61#12111yescharacteristic
317C2×C4×C61#12111yescharacteristic
318C2×C4×C61#12111yescharacteristic
319C2×C4×C61#12111yescharacteristic
320C2×C4×C61#12111yescharacteristic
321C2×C4×C61#12311yescharacteristic
322C2×C4×C61#12311yescharacteristic
323C2×C4×C61#12311yescharacteristic
324C2×C4×C61#12311yescharacteristic
325C2×C4×C61#12311yescharacteristic
326C2×C4×C61#12311yescharacteristic
327C2×C4×C61#12411yescharacteristic
328C2×C4×C61#12411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×Dic61—42no—
336C2×Dic61—82no—
337C8×C61—24no—
338#92418—24no—
339#92418—42no—
340#92418—42no—
341C2×#2048—611nomaximal, Sylow
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—42no—
350C22×C61—44no—
351C22×C61—82no—
352C22×C61—84no—
353C22×C61—82no—
354C22×C61—84no—
355C22×C61—84no—
356C22×C61—84no—
357C22×C61—84no—
358C22×C61—84no—
359C22×C61—82no—
360C22×C61—84no—
361C22×C61#39411yescharacteristic
362C22×C61#39411yescharacteristic
363C22×C61#39411yescharacteristic
364C22×C61#39411yescharacteristic
365C22×C61C2×#12111yescharacteristic
366C22×C61C2×#12311yescharacteristic
367C22×C61C2×#12411yescharacteristic
368C4×C61—42no—
369C4×C61#39411yescharacteristic
370C4×C61#39411yescharacteristic
371C4×C61#39411yescharacteristic
372C4×C61#39411yescharacteristic
373C4×C61C2×#12011yescharacteristic
374C4×C61C2×#12111yescharacteristic
375C4×C61C2×#12111yescharacteristic
376C4×C61C2×#12311yescharacteristic
377Dic61—82no—
378C22×AGL(1,ℤ/8)D6111yescharacteristic
379C2×#430—611no—
380C2×#421—611no—
381C2×#418—611no—
382C2×#413—611no—
383C22×#100—611no—
384#2048—618no—
385C2×#344—611no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—82no—
393C2×C61—84no—
394C2×C61#204812yescomplemented
395C2×C61C2×#39411yescharacteristic
396C22×#41C2×D6111yescharacteristic
397C23×D4C2×D6111yescharacteristic
398C2×AGL(1,ℤ/8)—22no—
399C2×AGL(1,ℤ/8)—22no—
400C2×AGL(1,ℤ/8)—22no—
401C2×AGL(1,ℤ/8)—22no—
402C2×AGL(1,ℤ/8)—22no—
403C2×AGL(1,ℤ/8)C2×D6114yes—
404C22×SD16—21no—
405C22×D8—21no—
406C22×M16—611no—
407C22×M16—611no—
408C22×M16—611no—
409C22×M16C2×D6111yescharacteristic
410C2×#117—611no—
411#430—614no—
412#430—1222no—
413C2×#108—1222no—
414#421—614no—
415#421—1222no—
416C2×#104—1222no—
417#418—614no—
418#418—1222no—
419C2×#102—1222no—
420#413—614no—
421#413—1222no—
422C2×#101—1221no—
423C2×#100—614no—
424C2×#100—1222no—
425C2×#100—1222no—
426C2×#100—1221no—
427#344—614no—
428C61C2×#204811yescharacteristic, complemented, Sylow
429C25—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41C22⋊D6112yes—
441C2×#41C22×D6112yes—
442C22×Q8C22⋊D6111yescharacteristic
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4C22⋊D6111yescharacteristic
456C22×D4C22⋊D6112yes—
457C22×D4C22⋊D6112yes—
458C22×D4C22×D6112yes—
459C23×C4—21no—
460C23×C4C22×D6111yescharacteristic
461AGL(1,ℤ/8)—28no—
462AGL(1,ℤ/8)—28no—
463AGL(1,ℤ/8)—28no—
464AGL(1,ℤ/8)—28no—
465C2×SD16—24no—
466C2×SD16—24no—
467C2×SD16—24no—
468C2×D8—24no—
469C2×D8—24no—
470C2×D8—24no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—612no—
475C2×M16—612no—
476C2×M16—612no—
477C2×M16—612no—
478C2×M16—612no—
479C2×M16—1221no—
480C2×M16—1221no—
481C2×M16—1221no—
482C2×M16—1221no—
483C2×M16—1221no—
484C2×M16—1221no—
485C2×M16—1221no—
486C2×M16—1221no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16—1221no—
492C2×M16C22⋊D6112yes—
493C2×M16C22⋊D6112yes—
494C2×M16C22×D6112yes—
495C22×C8—21no—
496C22×C8—1221no—
497C22×C8—1221no—
498C22×C8—1221no—
499#117—612no—
500#117—1221no—
501#117—1221no—
502#117—1221no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C42—1221no—
506#108—1228no—
507#104—1228no—
508#102—1228no—
509#101—1224no—
510#100—1228no—
511#100—1224no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—21no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24—41no—
520C24—84no—
521C24#1175822411yescharacteristic
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—41no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C22⋊D6112yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4C2×C22⋊D6112yes—
583C2×D4C2×C22⋊D6114yes—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—2441no—
592C22×C4D4×D6111yescharacteristic
593C22×C4D4×D6111yescharacteristic
594C22×C4#1175822411yescharacteristic
595C22×C4#1175822411yescharacteristic
596C22×C4#1175822411yescharacteristic
597C22×C4#1175822411yescharacteristic
598C22×C4#1175822411yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C23×D6111yescharacteristic
606SD16—216no—
607D8—216no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—614no—
612M16—1222no—
613M16—1222no—
614M16—1222no—
615M16—1222no—
616M16—1222no—
617M16—1222no—
618M16—1222no—
619M16—2441no—
620M16—2441no—
621M16—2441no—
622M16—2441no—
623M16C2×C22⋊D6114yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—1222no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—2441no—
633C2×C8—2441no—
634C2×C8—2441no—
635C2×C8—2441no—
636C4⋊C4—1222no—
637C4⋊C4—2441no—
638C22⋊C4—1222no—
639C22⋊C4—2441no—
640C42—1222no—
641C42—2441no—
642C23—24no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—82no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23#1451974911yescharacteristic
662C23#1451974911yescharacteristic
663C23#1451975811yescharacteristic
664C23#1451975811yescharacteristic
665C23#1451976411yescharacteristic
666C23#1451976411yescharacteristic
667C23C2×#1175822411yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—24no—
674D4—22no—
675D4—24no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—4882no—
696C2×C4—2442no—
697C2×C4#1451974611yescharacteristic
698C2×C4#1451974611yescharacteristic
699C2×C4#1451974611yescharacteristic
700C2×C4#1451974611yescharacteristic
701C2×C4#1451974811yescharacteristic
702C2×C4#1451974811yescharacteristic
703C2×C4#1451974811yescharacteristic
704C2×C4#1451974811yescharacteristic
705C2×C4#1451974911yescharacteristic
706C2×C4#1451974911yescharacteristic
707C2×C4#1451974911yescharacteristic
708C2×C4#1451974911yescharacteristic
709C2×C4#1451974911yescharacteristic
710C2×C4#1451974911yescharacteristic
711C2×C4#1451975811yescharacteristic
712C2×C4#1451975811yescharacteristic
713C2×C4#1451975811yescharacteristic
714C2×C4#1451975811yescharacteristic
715C2×C4#1451975811yescharacteristic
716C2×C4#1451975811yescharacteristic
717C2×C4#1451976411yescharacteristic
718C2×C4#1451976411yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4C22×C22⋊D6111yescharacteristic
721C2×C4C22×C22⋊D6111yescharacteristic
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C2×#1175822411yescharacteristic
724C2×C4C2×#1175822411yescharacteristic
725C8—24no—
726C8—1224no—
727C8—2442no—
728C8—2442no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—44no—
738C22—82no—
739C22—84no—
740C22—82no—
741C22—84no—
742C22—84no—
743C22—84no—
744C22—84no—
745C22—84no—
746C22—82no—
747C22—84no—
748C22#1683967611yescharacteristic
749C22#1683967611yescharacteristic
750C22#1683967611yescharacteristic
751C22#1683967611yescharacteristic
752C22C2×#1451974911yescharacteristic
753C22C2×#1451975811yescharacteristic
754C22C2×#1451976411yescharacteristic
755C4—42no—
756C4—4882no—
757C4#1683967611yescharacteristic
758C4#1683967611yescharacteristic
759C4#1683967611yescharacteristic
760C4#1683967611yescharacteristic
761C4C2×#1451974611yescharacteristic
762C4C2×#1451974811yescharacteristic
763C4C2×#1451974911yescharacteristic
764C4C2×#1451975811yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—84no—
772C2—82no—
773C2#2144708912yesdirect product factor
774C2C2×#1683967611yescharacteristic
subgroupG/H
centerC22#16839676
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC22×AGL(1,ℤ/8)×C61C2
socleC22×C61#394
hypercenterC22×AGL(1,ℤ/8)D61
hypocenterC61C2×#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16839810C2semidirect
2. C2×#16839779C2semidirect
3. C2×#16839767C2semidirect
4. C2×#16839746C2semidirect
5. C22×#14519694C2semidirect
6. #21447089C2direct (N × H)
7. C2×#16839534C2semidirect
14. #16839810C22semidirect
17. #16839779C22semidirect
20. #16839767C22semidirect
23. #16839746C22semidirect
28. C2×#14519694C22semidirect
29. #16839534C22semidirect
394. C2×C61#2048semidirect
428. C61C2×#2048semidirect
773. C2#21447089direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168398102
C2×#168397792
C2×#168397672
C2×#168397462
C22×#145196942
#214470892
C2×#168395342
C22×AGL(1,ℤ/8)×C612
C2×#204861